Check your cloud service provider terms and condition. Don't use them if you don't trust them. Yes, it is possible to create snapshot without shutting down, you can even do that with Virtualbox.
– mootmootJul 29 '16 at 17:25

Well, some cloud services allow you to encrypt the snapshot. But.....well, it is about trust.
– mootmootJul 29 '16 at 18:00

Many VPS providers allow you to access the console from where you can perform manual installation via PXE boot. This way you can install Linux from over internet (from mirror) and choose encrypted filesystem which makes imaging futile. The only thing they will be to do would be taking RAM snapshot and reading the key which is a bit harder.
– AriaJul 29 '16 at 21:36